Evaluation of Directed Causality Measures and Lag Estimations in Multivariate Time-Series

Abstract

The detection of causal effects among simultaneous observations provides knowledge about the underlying network, and is a topic of interests in many scientific areas. Over the years different causality measures have been developed, each with their own advantages and disadvantages. However, an extensive evaluation study is missing. In this work we consider some of the best-known causality measures i.e., cross-correlation, (conditional) Granger causality index (CGCI), partial directed coherence (PDC), directed transfer function (DTF), and partial mutual information on mixed embedding (PMIME). To correct for noise-related spurious connections, each measure (except PMIME) is tested for statistical significance based on surrogate data. The performance of the causality metrics is evaluated on a set of simulation models with distinct characteristics, to assess how well they work in- as well as outside of their “comfort zone.” PDC and DTF perform best on systems with frequency-specific connections, while PMIME is the only one able to detect non-linear interactions. The varying performance depending on the system characteristics warrants the use of multiple measures and comparing their results to avoid errors. Furthermore, lags between coupled variables are inherent to real-world systems and could hold essential information on the network dynamics. They are however often not taken into account and we lack proper tools to estimate them. We propose three new methods for lag estimation in multivariate time series, based on autoregressive modelling and information theory. One of the autoregressive methods and the one based on information theory were able to reliably identify the correct lag value in different simulated systems. However, only the latter was able to maintain its performance in the case of non-linear interactions. As a clinical application, the same methods are also applied on an intracranial recording of an epileptic seizure. The combined knowledge from the causality measures and insights from the simulations, on how these measures perform under different circumstances and when to use which one, allow us to recreate a plausible network of the seizure propagation that supports previous observations of desynchronisation and synchronisation during seizure progression. The lag estimation results show absence of a relationship between connectivity strength and estimated lag values, which contradicts the line of thinking in connectivity shaped by the neuron doctrine.

Physiological and pathological neuronal connectivity in the living human brain based on intracranial EEG signals: the current state of research

“…These methods, such as Granger causality and alternative causality measures designed on its background, for example, directed transfer function and partial directed coherence, are based on the statistical dependencies between different neuronal signals estimated on the basis of multivariate linear models or cross-spectral densities. They provide information about bidirectional interactions, thus quantifying the directed influence of signal x on signal y and vice versa (Chen et al, 2006;Kaminski et al, 2016;Heyse et al, 2021). Interpretation of estimated functional connectivity has to be performed with caution since there are several methodological issues that might influence the results (Friston et al, 2014;Bastos and Schoffelen, 2016).…”